直觉判断矩阵与区间互补判断矩阵的若干性质研究

发布时间：2018-11-24 09:27

【摘要】：在对方案或者属性进行两两比较的过程中,由于客观事物的不确定性和复杂性以及人类对事物认识的模糊性和自身知识的局限性,决策者往往给出的是不确定型的判断矩阵。常见的不确定型判断矩阵包括区间型判断矩阵、直觉判断矩阵等。关于这两类判断矩阵的研究主要集中在如何判定判断矩阵的一致性以及利用判断矩阵的一致性对方案进行排序等方面。一方面,本文研究了直觉判断矩阵的一致性与区间互补判断矩阵的一致性以及如何利用这些一致性确定方案的权重；另一方面,由于个体的差异性,决策者们对方案或者属性给出的偏好信息类型往往是不同的,例如模糊互补判断矩阵、区间互补判断矩阵、直觉判断矩阵,因此,本文也研究了区间互补判断矩阵、直觉判断矩阵转化为模糊互补判断矩阵的方法以及转化过程中的相关性质。本论文的主要研究内容如下：(1)研究了基于直觉判断矩阵有向图的方案排序方法。根据直觉模糊数的特点给出了直觉判断矩阵有向图的概念,并指出了直觉判断矩阵有向图有惟一有向路的条件。针对具有弱传递性的直觉判断矩阵,本文给出了一种基于直觉判断矩阵有向图的方案排序方法。(2)给出了直觉判断矩阵的加型一致性新定义与确定方案权重的方法。通过反例说明了直觉判断矩阵的加型一致性与直觉判断矩阵的弱传递性之间没有强弱关系,分析出其传统加型一致性定义的不足。根据直觉模糊数的特性提出了直觉判断矩阵加型一致性的新定义,并将之应用得到确定方案权重的中转法。另外,从直觉判断矩阵与权重之间的关系角度重新给出了直觉判断矩阵加型一致性的新定义并利用其确定权重。(3)研究了区间互补判断矩阵的拟一致性。分析了模糊互补判断矩阵的加型一致性和积型一致性,发现它们蕴含了相对优势度的特点,利用这个特点给出了区间互补判断矩阵的拟加型一致性、拟积型一致性概念。说明了它们本质上是相同的,因此统一地称之为区间互补判断矩阵拟一致性。分别针对拟一致性区间互补判断矩阵及一般的区间互补判断矩阵,建立了模型求解其区间数型权重。(4)研究了区间互补判断矩阵、直觉判断矩阵转化为模糊互补判断矩阵中的相关性质。针对模糊互补判断矩阵、区间互补判断矩阵、直觉判断矩阵给出了如何对这三种偏好关系进行一致化并进行集结的方法。首先分析了模糊互补判断矩阵的特点,利用这个特点将区间互补判断矩阵、直觉判断矩阵均转化为模糊互补判断矩阵,从而实现了这三类判断矩阵的一致化。然后研究了转换过程的合理性。
[Abstract]:In the process of comparing schemes or attributes, due to the uncertainty and complexity of objective things, the ambiguity of human cognition and the limitation of their own knowledge, the decision makers often give an uncertain judgment matrix. The common uncertain judgment matrix includes interval judgment matrix, intuitive judgment matrix and so on. The research on these two kinds of judgment matrices is mainly focused on how to judge the consistency of judgment matrices and how to use the consistency of judgment matrices to sort schemes. On the one hand, this paper studies the consistency of intuitionistic judgment matrix and interval complementary judgment matrix, and how to use these consistency to determine the weight of the scheme. On the other hand, due to individual differences, the preference information given by decision-makers to schemes or attributes is often different, such as fuzzy complementary judgment matrix, interval complementary judgment matrix, intuitive judgment matrix. This paper also studies the interval complementary judgment matrix, the method of transforming the intuitionistic judgment matrix into fuzzy complementary judgment matrix and the related properties in the process of transformation. The main contents of this thesis are as follows: (1) the scheme ordering method based on intuitionistic judgement matrix directed graph is studied. According to the characteristics of intuitionistic fuzzy numbers, the concept of directed graph of intuitionistic judgment matrix is given, and the condition that the directed graph of intuitionistic judgment matrix has unique directed path is pointed out. For the intuitionistic judgment matrix with weak transitivity, this paper presents a scheme ordering method based on directed graph of intuitionistic judgment matrix. (2) A new definition of additive consistency of intuitionistic judgment matrix and a method of determining scheme weight are given. It is shown that there is no strong or weak relation between additive consistency of intuitionistic judgment matrix and weak transitivity of intuitionistic judgment matrix by counterexample, and the deficiency of traditional definition of additive consistency is analyzed. According to the characteristics of intuitionistic fuzzy numbers, a new definition of additive consistency of intuitionistic judgment matrix is proposed and applied to the transfer method to determine the weight of the scheme. In addition, a new definition of additive consistency of intuitionistic judgment matrix is redefined from the angle of the relationship between intuitionistic judgment matrix and weight. (3) Quasi-consistency of interval complementary judgment matrix is studied. In this paper, the additive consistency and product consistency of fuzzy complementary judgment matrix are analyzed. It is found that they contain the characteristics of relative advantage degree. By using this characteristic, the concepts of quasi-additive consistency and quasi-product consistency of interval complementary judgment matrix are given. It is shown that they are essentially the same, so they are uniformly called quasi consistency of interval complementary judgment matrix. For the quasi-consistent interval complementary judgment matrix and the general interval complementary judgment matrix, the model is established to calculate the interval number type weights. (4) the interval complementary judgment matrix is studied. The intuitionistic judgment matrix is transformed into the correlation property of fuzzy complementary judgment matrix. Aiming at fuzzy complementary judgment matrix, interval complementary judgment matrix and intuitionistic judgment matrix, this paper gives a method of how to unify and assemble these three preference relations. Firstly, the characteristics of fuzzy complementary judgment matrix are analyzed, and the interval complementary judgment matrix and intuitionistic judgment matrix are transformed into fuzzy complementary judgment matrix by using this characteristic, thus realizing the uniformity of these three kinds of judgment matrices. Then the rationality of the conversion process is studied.
【学位授予单位】：合肥工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O151.21

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